A particle is dropped on Earth from height $R$ (radius of Earth) and it bounces back to a height $R/2$ the coefficient of restitution for collision is (ignore air resistance and rotation of Earth)

Two satellites $\mathrm{P}$ and $\mathrm{Q}$ are moving in different circular orbits around the Earth (radius $R$ ). The heights of $\mathrm{P}$ and $\mathrm{Q}$ from the Earth surface are $h_{\mathrm{p}}$ and $h_{\mathrm{Q}}$, respectively, where $h_{\mathrm{p}}=\mathrm{R} / 3$. The accelerations of $\mathrm{P}$ and $\mathrm{Q}$ due to Earth's gravity are $g_{\mathrm{p}}$ and $g_{\mathrm{Q}}$, respectively. If $g_{\mathrm{p}} / g_{\mathrm{Q}}=36 / 25$, what is the value of $h_Q$ ?

At what altitude in metre will the acceleration due to gravity be $25\%$ of that at the earth's surface (Radius of earth $= R\, metre$)

The mass of a planet is $\frac{1}{10}^{\text {th }}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

The weight of a body at the centre of the earth is